J . Phys. Chem. 1989, 93, 5963-5965 TABLE I: IR Band Intensities of Molecular Ions S,O, cm-* atm-' ion band expt theory HN2+
VI
HCO'
"I
Reference I O .
1250 (300)
3220" 2682b 751c 890d
430 (100)
Reference 1 1. Reference
12.
dReference 13
excitation are expected. Since hot bands have not been observed for HCO', its T, has been assumed to be the same as that observed for HN2+;this assumption is supported by the similarity in their measured rotational temperatures and in their vibrational frequencies. From the T, and T, measurements, Z;' and Z;' were calculated by using the standard equations* and used to determine Rir, and subsequently S:. Given the determinations of Sir,T,, and T,. the infrared band strengths were calculated for HN2+ and HCO', assuming the Herman-Wallis factor F to be unity. The absolute intensities for the v l bands are (to 1u ) 1250 (300) cm-2 atm-' for HN2+and 430 (100) cm-2 atm-' for HCO'. The largest contribution to the uncertainty is a result of the variation in Sirwith extraction voltage ( V e x ) .The values measured for Sirover the range Vex= 0.5-4.0 kV varied by a factor of 2, with higher Siffor lower Vex. The corresponding variations in T, (f100 K) were not large enough to compensate for the differences in Sir.The reproducibility in S: is closer to 10% with a particular set of conditions. The larger uncertainty quoted here accounts for possible systematic errors, principally those associated with Vex. Discussion The absolute IR band strength measurements presented for HN2+and HCO' are the first reported for molecular ions by direct absorption spectroscopy techniques. Indirect vibrational lifetime measurements have been performed,' including recent work on excited bending ( v 2 ) states of these same ions: but there are no (8) Herzberg, G.Infrared Spectra and Molecular Structure II. Infrared and Raman Spectra; Van Nostrand Reinhold: New York, 1945.
5963
experimental values available for the v I bands reported here. High-level a b initio calculations for the vibrational frequencies and intensities have been reported for HN2+by Kraemer et a1.I0 and Botschwina," and for HCO+ by Rogers and Hillmanlz and Bot~chwina.'~Our experimental values are lower than their theoretical counterparts by at least a factor of 2 for both molecules, as indicated in Table I, but the ratio of the values for HN2+ and HCO' (2.9 ( 5 ) ) is in excellent agreement with the predictions. Although the respective calculations published for the vI bands of each molecule are close to each other, those for other modes exhibit larger discrepancies. Even within the same tre'atment, different basis sets and different levels of theory lead to intensity predictions for the same mode that can vary by as much as a factor of three.'*" It is possible that the experimental values we report involve additional systematic errors associated with population of higher vibrational states that was not accounted for, or with effects due to ion extraction or to the treatment of the line widths, although these factors have been carefully examined in the present work. Additional experiments designed to further investigate these problems are in progress, as is the extension of these measurements to other ions, including H 3 0 + and NH4+. As absolute band strengths become available for more fundamental molecular ions, various other spectroscopic techniques can be used to directly monitor ion densities, in various environments, thus adding a new quantitative dimension to the spectroscopy of ions in the study of important chemical processes. Acknowledgment. This work was supported by the Experimental Physical Chemistry Program of the National Science Foundation (Grant CHE84-02861). We thank Ms. Nike Agman for her assistance in obtaining the data and thank Dr. Eldon Ferguson for communicating results before publication and for his useful comments on the subject. (9) Ferguson, E. E., private communication. ( I O ) Kraemer, W. P.; Komornicki, A,; Dixon, D. A. Chem. Phys. 1986, 105, 87. ( 1 1) Botschwina, P. Chem. Phys. Lett. 1984, 107, 535. (12) Rogers, J. D.; Hillman, J. J. J . Chem. Phys. 1982, 77, 3615. (13) Botschwina, P. J . Mol. Spectrosc. 1986, 110, 1.
Ultrafast Temperature Jump Studies of Hydrogen Bonds H. Graener* and T. Q. Ye Physikalisches Institut, Universitat Bayreuth. 0-8.580 Bayreuth, West Germany (Received: May 23, 1989)
Energy relaxation after vibrational excitation with picosecond IR pulses is necessarily accompanied by an overall temperature change. Whereas translational, rotational, and vibrational motions equilibrate faster than 50 ps for many systems, the hydrogen bonds may respond more slowly. We report on picosecond temperature jump experiments of the system ethanol:CCI4:CH2Brz using infrared excitation (10-ps pump pulses) and subsequent relaxation of the antenna molecules CH2Br2. The time evolutions of the OH stretching band of ethanol (3320 cm-') serve as spectroscopic probes to monitor hydrogen-bond breaking. The spontaneous lifetime of ethanol hydrogen bonds is determined for the first time by time-resolved spectroscopy yielding T = 240 f 50 ps.
Introduction Recently, we have demonstrated the feasibility of double-resOnance spectroscopy with independently tunable picosecond pulses.~.2 important application of this technique is the investigation of the dynamics of hydrogen bonds after ultrashort ( I ) Graener, H.; Dohlus, R.; Laubereau, A. Chem. Phys. Lett. 1987, 140,
excitation of the O H or also C H stretching modes. By use of the O H stretching frequencies as direct Probes of hydrogen bridges, vibrational predissociation and partial reassociation of ethanol oligomers was for the first time observed on the picosecond time scale. Different values for the dissociation rates and quantum yields provided strong evidence for mode specifity of the IR photodissociation in the liquid solution at room temperat~re.~An
306.
( 2 ) Graener, H.; Ye, T. Q.; Laubereau, A. J . Chem. Phys. 1989,90, 3413.
0022-3654/89/2093-5963$01.50/0
(3) Graener, H.; Ye, T. Q.; Laubereau, A. J . Chem. Phys., in press.
0 1989 American Chemical Society
5964
The Journal of Physical Chemistry, Vol. 93, No. 16, 1989
important question for these studies is the spontaneous lifetime of a hydrogen bond at thermal equilibrium. Only indirect information is atailable on this basic point from NMR, ultrasonic dispersion, and dielectric relaxation studies4 suggesting a time constant in the picosecond to nanosecond range while distinct spectroscopic data are lacking. In this Letter novel temperature jump experiments are reported on the thermal dissociation of hydrogen bridges of the system ethanol:CCL,. The O H stretching bands are used as direct spectroscopic probes of the H bonds, monitoring the transmission changes in the frequency range 3300-3600 cm-'. Ultrafast heating of the sample is realized by infrared pumping and subsequent thermalization of antenna molecules. It is known for several molecules that vibrational relaxation of C H stretching modes occurs with time constants shorter than 10 ps. Seilmeier et al. have further shown by ultrafast thermometry that the energy relaxation time was on the order of 10-20 ps for the investigated ~ y s t e m s . ~After this time most of the vibrational energy has relaxed and is transferred to translation and other degrees of freedom. The heating process will be discussed below in more detail. If the sample contains hydrogen-bonded molecules, the oligomer distribution will follow the temperature jump by dissociation and association processes according to the respective time constants. This chemical relaxation toward the new thermal equilibrium position can be observed via corresponding transmission changes in the IR spectrum, e.g., monitoring the O H stretching vibrations. The ultrashort time resolution of the probing mechanism has been demonstrated previously.
Letters
QHsOH
0.0
C
,
E
Our experimental system for ultrafast IR spectroscopy has been described recent1y.l An actively-passively mode-locked Nd:YAG laser with two amplifier stages generates single picosecond pulses with repetition rates up to 40 Hz. The strong tunable infrared pump pulses (duration 8 ps, bandwidth 8-15 cm-I, tuning range 2700-6500 cm-l, energy 1 0 0 MJ)are derived by a four-step parametric generator-amplifier setup from a large fraction of the Nd:YAG emission. The weak probe pulses (energy < 1 MJ)are generated in a separate double-step parametric system, which is pumped by the properly delayed remaining part of the original laser pulse. The two infrared pulses are focused into the thin sample cell (thickness 0.05-1 mm, depending on concentration). The energy transmission change In (TIT,) of the probe is measured as a function of delay time tD and of probe ( u ) and pump (up,,) frequencies. Here T(u ) denotes the transient probe transmission, while To ( u ) is the steady-state transmission value (pump beam blocked). In ( T / T o )serves as a direct measure of transient population effects and other spectral changes. The samples were ternary mixtures of spectral grade ethanol, solvent carbon tetrachloride, and antenna molecules methylene bromide. The pump frequency was tuned to 3070 cm-l, the strongly absorbing asymmetric C H stretching mode of CHZBr2. The population lifetime of this vibration is known to be T I = 7 f 1.5 ps6 and makes this molecule a good candidate for producing the desired fast temperature jump in the sample. Other degrees of freedom of the sample, in particular the chemical equilibrium of the hydrogen bridges, follow the sudden temperature change with their specific response times. The first experimental result, the transient response of the binary solution C2H50H:CC14(without CHzBr2heating), is depicted in Figure la. For the pump frequency up,, = 3070 cm-' residual absorption in the wing of the O H absorption band leads to a similar time evolution of In (TIT,) as observed previously for up,, = 3320 (4) Schuster, P.; Zundel, G.; Sandorfy, C.,Eds. T h e Hydrogen Bond Elsevier: Amsterdam, 1976; Vol. 3. Geisler, G.; Seidel, H. Die Wassersroffbrurkenbindung;Vieweg: Braunschweig, 1977, and references cited therein. ( 5 ) Seilmeier, A,; Kaiser, W .In Ultrafast Laser Pulses; Kaiser, W., Ed.; Springer-Verlag: Berlin, 1988; p 279 ff. (6) Graener, H.; Laubereau, A. Appl. Phys. 1982, B29, 213.
0.125 mf
CH&
P
4.
.
-
y1
n
b)
0 '
0
.
I
rD= K
t
240f30 ps
1
W' C+,OH
0.037 mf
CH$r2
0.308 mf
0
C)
0
Experiments and Results
0.043 mf
= 3070 cm-'
200
400
600
Delay Time
800
1000
[ps]
Figure 1. Relative transmission change of probe pulses with a frequency of 3320 cm-' versus delay time for different mixtures C2H50H:CH2Br2:CCI, (pump frequency 3070 cm-'; experimental, points; calculated, curves): (a) 0.043 mole fraction ethanol in carbon tetrachloride (without CH2Br2);(b) 0.037 mole fraction ethanol, 0.125 mole fraction methylene bromide; (c) 0.037 mole fraction ethanol, 0.3 1 methylene bromide.
cm-I but with considerably smaller amplitudes. The rapid rise and decay (time constant 20 ps) represents vibrational predissociation and reassociation of directly excited ethanol oligomers. The constant transmission change for tD > 200 ps suggests that the thermalization process of the ethanol molecules has already terminated and a new equilibrium of hydrogen-bonded chains is reached which is due to the temperature increase after partial absorption of the IR excitation pulse (CUI = 0.29 at 3070 cm-I). The results for the ternary mixture with two different concentrations of heating molecules CH2Br2(mole fraction x = 0.125 and 0.308) are presented in Figure 1 , b and c. The ethanol concentration is kept constant at 0.037 mole fraction. The strikingly different time dependence as compared to Figure l a should be noted. Besides the small signal spike at tD N 0 due to the direct ethanol excitation, a distinct transmission increase with rise time 7d = 220 ps is measured in Figure 1b. Increasing the methylene bromide (Figure IC), the fast absorption change due to the direct ethanol excitation becomes smaller, while the slow transmission increase due to the heating via CH2Br2molecules increases with approximately equal time constant s d and similar amplitudes as in Figure IC. It will be discussed below that 7 4 represents the (average) dissociation time constant of ethanol oligomers. We have studied the effect of ethanol concentration on the time constant T,,. The concentration of CH,Br, was kept constant (x = 0.25 mole fraction) in these measurements. When the ethanol concentration is increased from 0.21 to 1.28 mol/L, the dissociation time decreases from 220 to 150 ps. The results are summarized in Figure 2; the measured dissociation rate 1/7d is plotted versus concentration. Below 1.5 mol/L of ethanol, a linear dependence is observed within experimental accuracy. For larger ethanol concentration the observed relaxation rate increases more rapidly. This finding may be explained by V-V energy transfer from the C H vibration of CH,Br, to near-resonant C H vibrations of ethanol. As recently shown, the population of CH-stretching modes
The Journal of Physical Chemistry, Vol. 93, No. 16, 1989 5965
Letters
0.25 mf
The temperature change can be estimated from the transmission change at t D = 800 ps. Comparison with conventional (steadystate) IR transmission spectra gives an average temperature jump on the order of 10 K for Figure 1, b and c, with a1 = 3 and 7.4, respectively, at vPu = 3070 cm-l. The small signal amplitude of Figure l a (tD > 200 ps) nicely compares with the higher sample transmission a1 = 0.29 at 3070 cm-' of this measurement; Le., only 25% of the pump energy is absorbed and thermalized. Finally, we discuss in more detail the thermalization of the hydrogen bonds. The basic dissociation process of n-mer series pn to one or two other oligomers pPi and pi can be written as
CHZ Br2
44 z 3
0.0
0.5
1.o
Ethanol Concentration
1.5
[mol/l]
Figure 2. Effective dissociation rate versus ethanol concentration of the system C2HSOH:CH2Br2:CCl4. The concentration of the heating molecules CH2Br2was kept constant at 0.25 mole fraction.
of ethanol is followed by fast predissociation of hydrogen bonds within 15 ps. Analyzing this process suggests that for long times, fD > 80 ps, direct vibrational population effects have decayed by more than 2 orders of magnitude and have negligible influence on subsequent transmission changes. For this reason our data analysis for determining the r d values of Figure 2 is based on the observed transmission increase for long times, tD > 80 ps.
Discussion The sample heating following the picosecond C H excitation of the antenna molecules will be discussed first. Thermalizing of vibrational energy involves various processes: (i) V-V relaxation of the antenna molecules and direct transfer to ethanol vibrations, (ii) energy transfer to rotation and translation (V-R, V-T), (iii) thermalization within the rotational and translation degrees of freedom (R-R, R-T, T-T), and (iv) installation of the new chemical equilibrium. The short population lifetime of the excited C H mode gives evidence that vibrational relaxation (i) takes place within a few lo-" s. Equilibration of energy within rotational and translational degrees of freedom (processes iii), on the other hand, is expected to occur even faster. Available knowledge of orientation relaxation times and time constants derived from neutron scattering (velocity correlation times)' suggests thermalization within less than 10 ps. Fast energy exchange between rotational and translational motion is also obvious from ultrasonic dispersion data of liquids. The question remains about the role of V-R or V-T coupling. An answer is again supplied by ultrasonic dispersion results observing a relaxation frequency of 438 MHz (corresponding to T~~ N 360 ps) for CH,Br2 involving the vibrations 1576 cm-' while a faster component of the vibrational relaxation was attributed to the lowest vibration at 174 cm-1.8 These numbers together with detailed balance arguments suggest a time constant T~~ I 50 ps for the transfer of vibrational energy of CH2Br, to translation (and rotation). It is concluded that the heating of the ternary solution proceeds considerably faster than the dissociation of hydrogen bridges. (7) Kohler, F. The Liquid Slate; Verlag Chemie: Weinheim, 1972; p 157
ff. (8) Hunter, J. L.; Dardy, H. D. J . Chem. Phys. 1966, 44, 3637.
where kd and k, denote the dissociation and association rate constants. Case i = 0 describes the opening of a n-ring to a n-chain. In principle, the dissociation and association rates may vary with the size of the oligomers, the distribution of which is a function of ethanol concentration. Since such details are not known at the present time, we consider only average dissociation (kd) and association (k,) rates. The solution of the corresponding rate equation gives a time constant r , which accounts for the experimentally observed effective dissociation rateg 1 / T = kd kd(Cj)
+
wheref(cj) is a function depending on the concentrations cj of the dissociation products j . The functionf(cj) goes necessarily to zero with decreasing ethanol concentration. So the extrapolation toward zero ethanol concentration gives the dissociation rate kd. Our data of Figure 2 suggest a linear dependence of f ( c j ) yielding a spontaneous dissociation role of kd = 4.1 f 0.6 ns-'. Thus, the spontaneous lifetime of a hydrogen bond in ethanol is found to be T = 240 f 50 ps. It is interesting to compare this result with dielectric relaxation measurements. A relaxation time of 170 ps was determined from dispersion measurements of millimeter waves,1° which are in fair agreement with our data. We note that dielectric measurements may be influenced by various relaxation processes, whereas our spectroscopic result is clearly connected with the breaking of hydrogen bonds of oligomers.
Conclusions In summary, we point out that time-resolved IR spectroscopy is a useful tool for the determination of the dissociation rate of hydrogen bonds. The necessary temperature jump is produced by fast relaxation after absorption of a resonant picosecond pulse. The hydrogen bridges are monitored by measuring the O H stretching bands. From the concentration dependence of the thermal relaxation time the average lifetime of a hydrogen bridge of 240 ps is determined. Acknowledgment. The authors acknowledge with thanks the valuable discussions with A. Laubereau during the progress of the investigations. This work was supported by the Deutsche Forschungsgemeinschaft. (9) Tabuchi, D. J . Chem. Phys. 1957, 26, 993. (10) Saxton, J. A.; Bond, R. A.; Coats, G. T.; Dickinson, R. M. J . Chem. Phys. 1962, 37, 2132.
